Gamma Ray Pulsars: Emission from Extended Polar Cap Cascades

We have used a Monte Carlo simulation of a Polar Cap (PC) model of gamma-ray pulsars to estimate light curves and phase-resolved spectra for sources whose rotational and magnetic axes are oriented so that only one of the magnetic poles produces emission directed at the Earth. In this Single Polar Cap (SPC) scenario, even sources whose light curves have two distinct peaks (Crab, Vela, Geminga, PSR B1951+32) are due to emission concentrated near the rim of a single PC. If the inclination alpha is comparable to the half-width of the PC gamma-beam, alpha ~ theta_{b}, the peak-to-peak phase separation can have the large values (0.4 - 0.5) observed from these sources. In the model presented here we attribute the observed interpeak emission to pair cascades above the PC interior. Our simulation assumes the physics of conventional PC models, in which the gamma rays are due to photon-pair cascades initiated by curvature radiation from the acceleration of electrons above the PCs. In this work we assume that the acceleration occurs over a finite region which may extend up to several radii above the neutron star surface. We find that the combined effects of moderately enlarged PC dimensions and extended acceleration zones resolve a major difficulty with earlier PC models, namely their small beam widths (and hence small detection probabilities). Our best fits to the observed light curves are obtained from models in which the accelerated electrons have a uniform surface density over the PC interior and a sharp density increase of 3 - 5 near the rim.